Subgroups — C₂×#20257421 #27124274

Order 12032.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257421	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689839	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689826	C₂	1	2	yes	maximal, complemented
4	C₂×#15689821	C₂	1	2	yes	maximal, complemented
5	C₂×#15689795	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15689764	C₂	1	2	yes	maximal, complemented
7	C₂×#15689764	C₂	1	4	yes	maximal, complemented
8	C₂×D₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄×D₁₈₈	C₂	1	2	yes	maximal, complemented
10	C₂×#15689729	C₂	1	2	yes	maximal, complemented
11	C₂×#15689713	C₂	1	4	yes	maximal, complemented
12	C₂×#15689674	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15689660	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15689636	C₂	1	2	yes	maximal, complemented
15	C₂²×#13093999	C₂	1	2	yes	maximal, complemented
16	C₂×#15689595	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625354	C₂²	1	2	yes	complemented
20	C₂²×#10625354	C₂²	1	2	yes	complemented
21	C₂³×D₁₈₈	C₂²	1	2	yes	complemented
22	C₂³×D₁₈₈	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₄₇	C₂²	1	1	yes	characteristic
24	C₂²×D₄×D₄₇	C₂²	1	2	yes	—
25	C₂³×C₄×D₄₇	C₂²	1	2	yes	complemented
26	#15689839	C₂²	1	16	yes	complemented
27	#15689826	C₂²	1	32	yes	complemented
28	#15689821	C₂²	1	32	yes	complemented
29	#15689795	C₂²	1	16	yes	complemented
30	#15689764	C₂²	1	32	yes	complemented
31	#15689764	C₂²	1	64	yes	complemented
32	D₄×D₁₈₈	C₂²	1	16	yes	complemented
33	D₄×D₁₈₈	C₂²	1	32	yes	complemented
34	#15689729	C₂²	1	32	yes	complemented
35	#15689713	C₂²	1	64	yes	complemented
36	#15689674	C₂²	1	16	yes	complemented
37	C₂×#13094021	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13094021	C₂²	1	2	yes	complemented
39	#15689660	C₂²	1	16	yes	complemented
40	C₂×#13094019	C₂²	1	4	yes	complemented
41	C₂×#13094019	C₂²	1	2	yes	complemented
42	C₂×#13094015	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13094013	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13094013	C₂²	1	4	yes	complemented
45	C₂×#13094013	C₂²	1	2	yes	complemented
46	#15689636	C₂²	1	32	yes	complemented
47	C₂×#13094009	C₂²	1	2	yes	complemented
48	C₂×#13094009	C₂²	1	4	yes	complemented
49	C₂×#13094009	C₂²	1	4	yes	complemented
50	C₂×#13094009	C₂²	1	4	yes	complemented
51	C₂×#13094000	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13093999	C₂²	1	1	yes	characteristic
53	C₂×#13093999	C₂²	1	2	yes	complemented
54	C₂×#13093999	C₂²	1	2	yes	complemented
55	C₂×#13093999	C₂²	1	2	yes	complemented
56	C₂×#13093999	C₂²	1	4	yes	complemented
57	C₂×#13093999	C₂²	1	4	yes	complemented
58	C₂×#13093999	C₂²	1	2	yes	complemented
59	C₂×#13093999	C₂²	1	4	yes	complemented
60	C₂×#13093999	C₂²	1	2	yes	complemented
61	C₂×#13093999	C₂²	1	2	yes	complemented
62	C₂×#13093999	C₂²	1	4	yes	complemented
63	C₂×#13093999	C₂²	1	32	yes	complemented
64	C₂×#13093998	C₂²	1	2	yes	complemented
65	C₂×#13093998	C₂²	1	4	yes	complemented
66	C₂×#13093994	C₂²	1	4	yes	complemented
67	C₂×#13093994	C₂²	1	4	yes	complemented
68	C₂×#13093994	C₂²	1	4	yes	complemented
69	#15689595	C₂²	1	32	yes	complemented
70	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
72	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
73	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
74	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
75	C₂×#13093986	C₂²	1	1	yes	characteristic, complemented
76	C₂×#13093986	C₂²	1	2	yes	complemented
77	C₂×#13093986	C₂²	1	4	yes	complemented
78	C₂×#13093986	C₂²	1	2	yes	complemented
79	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
80	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
81	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
82	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
83	C₄×D₄×D₄₇	C₂²	1	16	yes	complemented
84	C₂×#13093982	C₂²	1	2	yes	complemented
85	C₂×#13093982	C₂²	1	2	yes	complemented
86	C₂×#13093981	C₂²	1	2	yes	complemented
87	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
88	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	complemented
89	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
90	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
91	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₄₇×#554	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₂×#125×C₄₇	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
96	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
97	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
99	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
100	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂⁴×D₄₇	C₂³	1	4	yes	—
103	C₂×#10625354	—	4	8	no	—
104	C₂×#10625354	—	4	8	no	—
105	C₂×#10625354	C₂³	1	16	yes	complemented
106	C₂×#10625354	C₂³	1	16	yes	complemented
107	C₂²×D₁₈₈	—	4	8	no	—
108	C₂²×D₁₈₈	—	4	16	no	—
109	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
110	C₂²×D₁₈₈	C₂³	1	2	yes	—
111	C₂²×D₁₈₈	C₂³	1	4	yes	—
112	C₂²×D₁₈₈	C₂³	1	2	yes	—
113	C₂²×D₁₈₈	C₂³	1	2	yes	—
114	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
115	C₂²×D₁₈₈	C₂³	1	4	yes	—
116	C₂²×D₁₈₈	C₂³	1	2	yes	—
117	C₂²×D₁₈₈	C₂³	1	4	yes	—
118	C₂²×D₁₈₈	C₂³	1	4	yes	—
119	C₂²×D₁₈₈	C₂³	1	4	yes	—
120	C₂²×D₁₈₈	C₂³	1	16	yes	complemented
121	C₂²×D₁₈₈	C₂³	1	32	yes	complemented
122	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
123	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
124	C₂×D₄×D₄₇	—	2	8	no	—
125	C₂×D₄×D₄₇	—	2	16	no	—
126	C₂×D₄×D₄₇	C₂³	1	8	yes	—
127	C₂×D₄×D₄₇	C₂³	1	16	yes	—
128	C₂³×Dic₄₇	C₂³	1	2	yes	—
129	C₂²×C₄×D₄₇	—	4	8	no	—
130	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
133	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
134	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
137	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
138	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
139	C₂²×C₄×D₄₇	C₂³	1	16	yes	complemented
140	#13094021	C₂³	1	16	yes	complemented
141	#13094021	C₂³	1	8	yes	complemented
142	#13094019	C₂³	1	32	yes	complemented
143	#13094019	C₂³	1	16	yes	complemented
144	#13094015	C₂³	1	8	yes	complemented
145	#13094013	C₂³	1	8	yes	complemented
146	#13094013	C₂³	1	32	yes	complemented
147	#13094013	C₂³	1	16	yes	complemented
148	#13094009	C₂³	1	32	yes	complemented
149	#13094009	C₂³	1	32	yes	complemented
150	#13094009	C₂³	1	16	yes	complemented
151	#13094009	C₂³	1	32	yes	complemented
152	#13094000	C₂³	1	8	yes	complemented
153	#13093999	C₂³	1	8	yes	—
154	#13093999	C₂³	1	16	yes	complemented
155	#13093999	C₂³	1	16	yes	complemented
156	#13093999	C₂³	1	32	yes	complemented
157	#13093999	C₂³	1	32	yes	complemented
158	#13093999	C₂³	1	16	yes	complemented
159	#13093999	C₂³	1	32	yes	complemented
160	#13093999	C₂³	1	32	yes	complemented
161	#13093999	C₂³	1	16	yes	complemented
162	#13093999	C₂³	1	16	yes	complemented
163	#13093999	C₂³	1	16	yes	complemented
164	#13093998	C₂³	1	16	yes	complemented
165	#13093998	C₂³	1	32	yes	complemented
166	#13093994	C₂³	1	32	yes	complemented
167	#13093994	C₂³	1	32	yes	complemented
168	#13093994	C₂³	1	32	yes	complemented
169	C₄×D₁₈₈	C₂³	1	16	yes	complemented
170	C₄×D₁₈₈	C₂³	1	8	yes	complemented
171	C₄×D₁₈₈	C₂³	1	16	yes	complemented
172	C₄×D₁₈₈	C₂³	1	8	yes	complemented
173	D₄×Dic₄₇	C₂³	1	8	yes	—
174	#13093986	C₂³	1	8	yes	complemented
175	#13093986	C₂³	1	16	yes	complemented
176	#13093986	C₂³	1	16	yes	complemented
177	#13093986	C₂³	1	32	yes	complemented
178	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
179	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
180	(C₂²⋊D₄₇)⋊C₄	C₂³	1	16	yes	complemented
181	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
182	#13093982	C₂³	1	16	yes	complemented
183	#13093982	C₂³	1	16	yes	complemented
184	#13093981	C₂³	1	16	yes	complemented
185	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
188	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
189	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
190	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
191	C₄⋊C₄×D₄₇	C₂³	1	8	yes	complemented
192	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
198	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
199	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
200	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
201	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
202	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
203	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
204	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
205	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
206	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	complemented
207	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	complemented
208	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
209	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
210	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
211	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
212	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
213	C₄²×D₄₇	C₂³	1	8	yes	complemented
214	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
215	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
216	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
217	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
218	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
219	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
220	#125×C₄₇	C₂³	1	16	yes	complemented
221	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
222	C₂²⋊Q₈×C₄₇	C₂³	1	32	yes	complemented
223	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
224	C₄×D₄×C₄₇	C₂³	1	8	yes	—
225	C₄×D₄×C₄₇	C₂³	1	16	yes	—
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
233	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	complemented
234	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
235	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
236	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
237	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
238	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
239	C₂³×D₄₇	—	2	8	no	—
240	C₂³×D₄₇	—	2	16	no	—
241	C₂³×D₄₇	—	2	8	no	—
242	C₂³×D₄₇	—	4	4	no	—
243	C₂³×D₄₇	—	4	8	no	—
244	C₂³×D₄₇	—	4	8	no	—
245	C₂³×D₄₇	C₂⁴	1	2	yes	—
246	C₂³×D₄₇	C₂⁴	1	2	yes	—
247	C₂³×D₄₇	C₂⁴	1	4	yes	—
248	C₂³×D₄₇	C₂⁴	1	8	yes	—
249	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
250	C₂³×D₄₇	C₂⁴	1	16	yes	—
251	C₂×Q₈×C₄₇	—	2	4	no	—
252	C₂×Q₈×C₄₇	—	4	4	no	—
253	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
255	C₂×D₄×C₄₇	#41	1	8	yes	complemented
256	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₄₇	—	2	8	no	—
258	C₂²×C₄×C₄₇	—	4	8	no	—
259	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
266	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂×C₂²⋊D₄₇	—	2	8	no	—
269	C₂×C₂²⋊D₄₇	—	2	16	no	—
270	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
271	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
272	C₂²×Dic₄₇	—	4	4	no	—
273	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
274	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
275	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
276	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
277	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
278	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
279	#10625354	—	4	32	no	—
280	#10625354	—	4	32	no	—
281	D₄×D₄₇	—	2	32	no	—
282	D₄×D₄₇	—	2	64	no	—
283	C₂×D₁₈₈	—	2	8	no	—
284	C₂×D₁₈₈	—	2	16	no	—
285	C₂×D₁₈₈	—	2	4	no	—
286	C₂×D₁₈₈	—	2	8	no	—
287	C₂×D₁₈₈	—	2	4	no	—
288	C₂×D₁₈₈	—	2	8	no	—
289	C₂×D₁₈₈	—	4	32	no	—
290	C₂×D₁₈₈	—	4	64	no	—
291	C₂×D₁₈₈	—	4	8	no	—
292	C₂×D₁₈₈	—	4	8	no	—
293	C₂×D₁₈₈	—	4	8	no	—
294	C₂×D₁₈₈	—	4	4	no	—
295	C₂×D₁₈₈	—	4	8	no	—
296	C₂×D₁₈₈	C₂⁴	1	4	yes	—
297	C₂×D₁₈₈	C₂⁴	1	8	yes	—
298	C₂×D₁₈₈	C₂⁴	1	16	yes	—
299	C₂×D₁₈₈	C₂⁴	1	8	yes	—
300	C₂×D₁₈₈	C₂⁴	1	8	yes	—
301	C₂×D₁₈₈	C₂⁴	1	4	yes	—
302	C₂×D₁₈₈	C₂⁴	1	16	yes	—
303	C₂×D₁₈₈	C₂⁴	1	8	yes	—
304	C₂×D₁₈₈	C₂⁴	1	16	yes	—
305	C₂×D₁₈₈	C₂⁴	1	16	yes	—
306	C₂×D₁₈₈	C₂⁴	1	16	yes	—
307	C₂×C₄×D₄₇	—	2	4	no	—
308	C₂×C₄×D₄₇	—	2	4	no	—
309	C₂×C₄×D₄₇	—	2	8	no	—
310	C₂×C₄×D₄₇	—	2	4	no	—
311	C₂×C₄×D₄₇	—	2	8	no	—
312	C₂×C₄×D₄₇	—	4	32	no	—
313	C₂×C₄×D₄₇	—	4	4	no	—
314	C₂×C₄×D₄₇	—	4	4	no	—
315	C₂×C₄×D₄₇	—	4	8	no	—
316	C₂×C₄×D₄₇	—	4	8	no	—
317	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
318	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
319	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
320	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
321	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
322	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
323	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
324	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
325	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
326	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
328	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
329	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
332	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
333	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
334	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
335	C₄²×C₄₇	C₂⁴	1	8	yes	—
336	C₄²×C₄₇	C₂⁴	1	4	yes	—
337	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
338	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
339	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
340	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
341	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
342	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
343	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
344	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
345	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
346	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
347	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
348	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
349	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
350	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
351	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
352	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
353	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
354	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
355	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
356	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
357	C₄×Dic₄₇	C₂⁴	1	4	yes	—
358	C₄×Dic₄₇	C₂⁴	1	4	yes	—
359	C₄×Dic₄₇	C₂⁴	1	4	yes	—
360	C₄×Dic₄₇	C₂⁴	1	16	yes	—
361	C₂³×C₄₇	—	2	4	no	—
362	C₂³×C₄₇	—	2	4	no	—
363	C₂³×C₄₇	C₂×#41	1	8	yes	—
364	C₂³×C₄₇	C₂⁵	1	4	yes	—
365	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
366	C₂²×D₄₇	—	2	2	no	—
367	C₂²×D₄₇	—	2	2	no	—
368	C₂²×D₄₇	—	2	4	no	—
369	C₂²×D₄₇	—	2	4	no	—
370	C₂²×D₄₇	—	2	8	no	—
371	C₂²×D₄₇	—	2	16	no	—
372	C₂²×D₄₇	—	2	4	no	—
373	C₂²×D₄₇	—	2	8	no	—
374	C₂²×D₄₇	—	2	8	no	—
375	C₂²×D₄₇	—	2	4	no	—
376	C₂²×D₄₇	—	2	4	no	—
377	C₂²×D₄₇	—	2	4	no	—
378	C₂²×D₄₇	—	2	32	no	—
379	C₂²×D₄₇	—	2	16	no	—
380	C₂²×D₄₇	—	4	8	no	—
381	C₂²×D₄₇	—	4	16	no	—
382	C₂²×D₄₇	—	4	16	no	—
383	C₂²×D₄₇	—	4	32	no	—
384	C₂²×D₄₇	—	8	32	no	—
385	C₂²×D₄₇	H(5,𝔽₂)	1	4	yes	—
386	C₂²×D₄₇	C₂⁵	1	4	yes	—
387	C₂²×D₄₇	C₂⁵	1	4	yes	—
388	C₂²×D₄₇	C₂⁵	1	8	yes	—
389	C₂²×D₄₇	C₂⁵	1	2	yes	—
390	Q₈×C₄₇	—	2	8	no	—
391	Q₈×C₄₇	—	4	8	no	—
392	D₄×C₄₇	C₂×#41	1	16	yes	complemented
393	C₂×C₄×C₄₇	—	2	2	no	—
394	C₂×C₄×C₄₇	—	2	4	no	—
395	C₂×C₄×C₄₇	—	2	4	no	—
396	C₂×C₄×C₄₇	—	2	8	no	—
397	C₂×C₄×C₄₇	—	2	4	no	—
398	C₂×C₄×C₄₇	—	2	16	no	—
399	C₂×C₄×C₄₇	—	4	16	no	—
400	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
401	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
402	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
403	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
404	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
405	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
406	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
407	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
408	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
409	C₂²⋊D₄₇	—	2	16	no	—
410	C₂²⋊D₄₇	—	2	32	no	—
411	C₂×Dic₄₇	—	2	2	no	—
412	C₂×Dic₄₇	—	2	4	no	—
413	C₂×Dic₄₇	—	2	2	no	—
414	C₂×Dic₄₇	—	2	4	no	—
415	C₂×Dic₄₇	—	2	2	no	—
416	C₂×Dic₄₇	—	4	8	no	—
417	C₂×Dic₄₇	C₂⁵	1	2	yes	—
418	C₂×Dic₄₇	C₂⁵	1	4	yes	—
419	C₂×Dic₄₇	C₂⁵	1	2	yes	—
420	C₂×Dic₄₇	C₂⁵	1	2	yes	—
421	C₂×Dic₄₇	C₂⁵	1	4	yes	—
422	D₁₈₈	—	2	16	no	—
423	D₁₈₈	—	2	32	no	—
424	D₁₈₈	—	2	8	no	—
425	D₁₈₈	—	2	16	no	—
426	D₁₈₈	—	2	8	no	—
427	D₁₈₈	—	2	16	no	—
428	D₁₈₈	—	4	16	no	—
429	D₁₈₈	—	4	16	no	—
430	D₁₈₈	—	4	16	no	—
431	D₁₈₈	—	4	8	no	—
432	D₁₈₈	—	4	16	no	—
433	C₄×D₄₇	—	2	8	no	—
434	C₄×D₄₇	—	2	8	no	—
435	C₄×D₄₇	—	2	16	no	—
436	C₄×D₄₇	—	2	8	no	—
437	C₄×D₄₇	—	2	16	no	—
438	C₄×D₄₇	—	4	8	no	—
439	C₄×D₄₇	—	4	8	no	—
440	C₄×D₄₇	—	4	16	no	—
441	C₄×D₄₇	—	4	16	no	—
442	C₂×#3519	—	47	1	no	maximal, Sylow
443	C₂²×C₄₇	—	2	4	no	—
444	C₂²×C₄₇	—	2	4	no	—
445	C₂²×C₄₇	—	2	16	no	—
446	C₂²×C₄₇	C₂²×#41	1	8	yes	—
447	C₂²×C₄₇	C₂²×#41	1	2	yes	—
448	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
450	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
451	C₂×D₄₇	—	2	2	no	—
452	C₂×D₄₇	—	2	2	no	—
453	C₂×D₄₇	—	2	8	no	—
454	C₂×D₄₇	—	2	4	no	—
455	C₂×D₄₇	—	2	4	no	—
456	C₂×D₄₇	—	2	8	no	—
457	C₂×D₄₇	—	2	4	no	—
458	C₂×D₄₇	—	2	8	no	—
459	C₂×D₄₇	—	2	8	no	—
460	C₂×D₄₇	—	2	4	no	—
461	C₂×D₄₇	—	2	4	no	—
462	C₂×D₄₇	—	2	4	no	—
463	C₂×D₄₇	—	4	32	no	—
464	C₂×D₄₇	—	4	8	no	—
465	C₂×D₄₇	—	4	16	no	—
466	C₂×D₄₇	—	4	8	no	—
467	C₂×D₄₇	—	8	32	no	—
468	C₂×D₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
469	C₄×C₄₇	—	2	2	no	—
470	C₄×C₄₇	—	2	4	no	—
471	C₄×C₄₇	—	2	4	no	—
472	C₄×C₄₇	—	2	8	no	—
473	C₄×C₄₇	—	2	4	no	—
474	C₄×C₄₇	C₂²×#41	1	4	yes	—
475	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
476	Dic₄₇	—	2	2	no	—
477	Dic₄₇	—	2	4	no	—
478	Dic₄₇	—	2	2	no	—
479	Dic₄₇	—	2	4	no	—
480	Dic₄₇	—	2	2	no	—
481	#3519	—	47	32	no	—
482	C₂×#555	—	47	1	no	—
483	C₂×#554	D₄₇	1	1	yes	characteristic, complemented
484	C₂×#553	—	47	2	no	—
485	C₂×#553	—	47	2	no	—
486	C₂×#550	—	47	1	no	—
487	C₂×#546	—	47	4	no	—
488	C₂×#546	—	47	2	no	—
489	C₂×D₄²	—	47	2	no	—
490	C₂×D₄²	—	47	1	no	—
491	C₂×#540	—	47	2	no	—
492	C₂×#538	—	47	4	no	—
493	C₂×#532	—	47	1	no	—
494	C₂×#529	—	47	1	no	—
495	C₂×#525	—	47	2	no	—
496	C₂²×#121	—	47	2	no	—
497	C₂×#518	—	47	2	no	—
498	C₂²×C₄×D₄	—	47	1	no	—
499	C₂×C₄₇	—	2	8	no	—
500	C₂×C₄₇	#3519	1	4	yes	complemented
501	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
502	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
504	D₄₇	—	2	4	no	—
505	D₄₇	—	4	4	no	—
506	D₄₇	—	4	8	no	—
507	D₄₇	—	4	4	no	—
508	C₂²×#41	—	47	2	no	—
509	C₂²×#41	—	47	2	no	—
510	C₂³×D₄	—	47	1	no	—
511	C₂³×D₄	—	47	2	no	—
512	C₂³×D₄	—	47	2	no	—
513	C₂³×D₄	—	47	4	no	—
514	C₂⁴×C₄	—	47	2	no	—
515	#555	—	47	16	no	—
516	#554	C₂×D₄₇	1	16	yes	complemented
517	#553	—	47	32	no	—
518	#553	—	47	32	no	—
519	#550	—	47	16	no	—
520	#546	—	47	64	no	—
521	#546	—	47	32	no	—
522	D₄²	—	47	32	no	—
523	D₄²	—	47	16	no	—
524	#540	—	47	32	no	—
525	#538	—	47	64	no	—
526	#532	—	47	16	no	—
527	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
528	C₂×#127	—	47	1	no	—
529	C₂×#127	—	47	2	no	—
530	#529	—	47	16	no	—
531	C₂×#126	—	47	2	no	—
532	C₂×#126	—	47	4	no	—
533	C₂×#125	—	47	1	no	—
534	C₂×#125	C₂×D₄₇	1	2	yes	complemented
535	C₂×#124	—	47	1	no	—
536	C₂×#124	—	47	2	no	—
537	C₂×#124	—	47	4	no	—
538	#525	—	47	32	no	—
539	C₂×#123	—	47	4	no	—
540	C₂×#123	—	47	2	no	—
541	C₂×#123	—	47	4	no	—
542	C₂×#123	—	47	4	no	—
543	C₂×C₂²⋊Q₈	—	47	1	no	—
544	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
545	C₂×C₂²⋊Q₈	C₂×D₄₇	1	4	yes	complemented
546	C₂×#121	—	47	2	no	—
547	C₂×#121	—	47	4	no	—
548	C₂×#121	—	47	1	no	—
549	C₂×#121	—	47	2	no	—
550	C₂×#121	—	47	4	no	—
551	C₂×#121	—	47	4	no	—
552	C₂×#121	—	47	2	no	—
553	C₂×#121	—	47	2	no	—
554	C₂×#121	—	47	2	no	—
555	C₂×#121	—	47	4	no	—
556	C₂×#121	—	47	2	no	—
557	C₂×#121	—	47	2	no	—
558	C₂×#121	—	47	4	no	—
559	C₂×#121	—	47	32	no	—
560	C₂×#120	—	47	4	no	—
561	C₂×#120	—	47	4	no	—
562	C₂×#120	—	47	4	no	—
563	#518	—	47	32	no	—
564	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
565	C₂×C₄×D₄	—	47	1	no	—
566	C₂×C₄×D₄	—	47	2	no	—
567	C₂×C₄×D₄	—	47	4	no	—
568	C₂×C₄×D₄	—	47	16	no	—
569	C₂×C₄×D₄	—	47	1	no	—
570	C₂×C₄×D₄	—	47	2	no	—
571	C₂×C₄×D₄	—	47	4	no	—
572	C₂×C₄×D₄	—	47	2	no	—
573	C₂×C₄×D₄	—	47	2	no	—
574	C₂×C₄×D₄	—	47	4	no	—
575	C₂×C₄×D₄	—	47	1	no	—
576	C₂×C₄×D₄	—	47	2	no	—
577	C₂×C₄×D₄	—	47	2	no	—
578	C₂×C₄×D₄	—	47	1	no	—
579	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
580	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
581	C₂×#117	—	47	2	no	—
582	C₂×#117	—	47	2	no	—
583	C₂×#117	—	47	2	no	—
584	C₂²×C₄⋊C₄	—	47	1	no	—
585	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
586	C₂²×C₂²⋊C₄	—	47	4	no	—
587	C₂²×C₂²⋊C₄	—	47	2	no	—
588	C₂²×C₂²⋊C₄	—	47	4	no	—
589	C₂²×C₄²	—	47	1	no	—
590	C₄₇	C₂×#3519	1	1	yes	characteristic, complemented, Sylow
591	C₂⁵	—	47	2	no	—
592	C₂⁵	—	47	4	no	—
593	C₂×#41	—	47	16	no	—
594	C₂×#41	—	47	16	no	—
595	C₂×#41	—	188	8	no	—
596	C₂×#41	—	188	8	no	—
597	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
598	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
599	C₂²×D₄	—	47	2	no	—
600	C₂²×D₄	—	47	4	no	—
601	C₂²×D₄	—	47	8	no	—
602	C₂²×D₄	—	47	16	no	—
603	C₂²×D₄	—	47	1	no	—
604	C₂²×D₄	—	47	2	no	—
605	C₂²×D₄	—	47	4	no	—
606	C₂²×D₄	—	47	2	no	—
607	C₂²×D₄	—	47	1	no	—
608	C₂²×D₄	—	47	2	no	—
609	C₂²×D₄	—	47	4	no	—
610	C₂²×D₄	—	47	2	no	—
611	C₂²×D₄	—	47	4	no	—
612	C₂²×D₄	—	47	4	no	—
613	C₂²×D₄	—	47	4	no	—
614	C₂²×D₄	—	47	16	no	—
615	C₂²×D₄	—	47	32	no	—
616	C₂²×D₄	—	94	16	no	—
617	C₂²×D₄	—	94	8	no	—
618	C₂²×D₄	—	188	8	no	—
619	C₂²×D₄	—	188	16	no	—
620	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
621	C₂³×C₄	—	47	2	no	—
622	C₂³×C₄	—	47	1	no	—
623	C₂³×C₄	—	47	1	no	—
624	C₂³×C₄	—	47	2	no	—
625	C₂³×C₄	—	47	2	no	—
626	C₂³×C₄	—	47	1	no	—
627	C₂³×C₄	—	47	2	no	—
628	C₂³×C₄	—	47	4	no	—
629	C₂³×C₄	—	47	4	no	—
630	C₂³×C₄	—	47	2	no	—
631	C₂³×C₄	—	47	16	no	—
632	C₂³×C₄	—	188	8	no	—
633	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
634	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
635	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
636	#127	—	47	8	no	—
637	#127	—	47	16	no	—
638	#126	—	47	16	no	—
639	#126	—	47	32	no	—
640	#125	—	47	8	no	—
641	#125	C₂²×D₄₇	1	16	yes	complemented
642	#124	—	47	8	no	—
643	#124	—	47	16	no	—
644	#124	—	47	32	no	—
645	#123	—	47	32	no	—
646	#123	—	47	16	no	—
647	#123	—	47	32	no	—
648	#123	—	47	32	no	—
649	C₂²⋊Q₈	—	47	8	no	—
650	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
651	C₂²⋊Q₈	C₂²×D₄₇	1	32	yes	complemented
652	#121	—	47	16	no	—
653	#121	—	47	32	no	—
654	#121	—	47	8	no	—
655	#121	—	47	16	no	—
656	#121	—	47	32	no	—
657	#121	—	47	32	no	—
658	#121	—	47	16	no	—
659	#121	—	47	16	no	—
660	#121	—	47	16	no	—
661	#121	—	47	32	no	—
662	#121	—	47	16	no	—
663	#121	—	47	16	no	—
664	#121	—	47	32	no	—
665	#120	—	47	32	no	—
666	#120	—	47	32	no	—
667	#120	—	47	32	no	—
668	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
669	C₄×D₄	—	47	8	no	—
670	C₄×D₄	—	47	16	no	—
671	C₄×D₄	—	47	32	no	—
672	C₄×D₄	—	47	8	no	—
673	C₄×D₄	—	47	16	no	—
674	C₄×D₄	—	47	32	no	—
675	C₄×D₄	—	47	16	no	—
676	C₄×D₄	—	47	16	no	—
677	C₄×D₄	—	47	32	no	—
678	C₄×D₄	—	47	8	no	—
679	C₄×D₄	—	47	16	no	—
680	C₄×D₄	—	47	16	no	—
681	C₄×D₄	—	47	8	no	—
682	C₄×D₄	C₂²×D₄₇	1	8	yes	—
683	C₄×D₄	C₂²×D₄₇	1	16	yes	—
684	#117	—	47	16	no	—
685	#117	—	47	16	no	—
686	#117	—	47	16	no	—
687	C₂×C₄⋊C₄	—	47	1	no	—
688	C₂×C₄⋊C₄	—	47	2	no	—
689	C₂×C₄⋊C₄	—	47	1	no	—
690	C₂×C₄⋊C₄	—	47	2	no	—
691	C₂×C₄⋊C₄	—	47	2	no	—
692	C₂×C₄⋊C₄	—	47	2	no	—
693	C₂×C₄⋊C₄	—	47	8	no	—
694	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
697	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
698	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
700	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
701	C₂×C₄⋊C₄	C₂²×D₄₇	1	16	yes	complemented
702	C₂×C₂²⋊C₄	—	47	2	no	—
703	C₂×C₂²⋊C₄	—	47	2	no	—
704	C₂×C₂²⋊C₄	—	47	4	no	—
705	C₂×C₂²⋊C₄	—	47	2	no	—
706	C₂×C₂²⋊C₄	—	47	4	no	—
707	C₂×C₂²⋊C₄	—	47	2	no	—
708	C₂×C₂²⋊C₄	—	47	4	no	—
709	C₂×C₂²⋊C₄	—	47	2	no	—
710	C₂×C₂²⋊C₄	—	47	32	no	—
711	C₂×C₂²⋊C₄	—	47	4	no	—
712	C₂×C₂²⋊C₄	—	47	2	no	—
713	C₂×C₂²⋊C₄	—	47	2	no	—
714	C₂×C₂²⋊C₄	—	47	2	no	—
715	C₂×C₂²⋊C₄	—	47	4	no	—
716	C₂×C₂²⋊C₄	—	47	4	no	—
717	C₂×C₂²⋊C₄	—	47	16	no	—
718	C₂×C₂²⋊C₄	—	47	32	no	—
719	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
721	C₂×C₄²	—	47	1	no	—
722	C₂×C₄²	—	47	4	no	—
723	C₂×C₄²	—	47	1	no	—
724	C₂×C₄²	—	47	1	no	—
725	C₂×C₄²	—	47	8	no	—
726	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
727	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
728	C₂⁴	—	47	1	no	—
729	C₂⁴	—	47	2	no	—
730	C₂⁴	—	47	4	no	—
731	C₂⁴	—	47	2	no	—
732	C₂⁴	—	47	8	no	—
733	C₂⁴	—	47	16	no	—
734	C₂⁴	—	94	8	no	—
735	C₂⁴	—	94	16	no	—
736	C₂⁴	—	94	8	no	—
737	C₂⁴	—	188	8	no	—
738	C₂⁴	—	188	8	no	—
739	C₂⁴	—	188	4	no	—
740	C₂⁴	C₂³×D₄₇	1	2	yes	—
741	#41	—	188	32	no	—
742	#41	—	188	32	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	4	4	no	—
745	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
746	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
747	C₂×D₄	—	47	8	no	—
748	C₂×D₄	—	47	16	no	—
749	C₂×D₄	—	47	4	no	—
750	C₂×D₄	—	47	8	no	—
751	C₂×D₄	—	47	16	no	—
752	C₂×D₄	—	47	8	no	—
753	C₂×D₄	—	47	4	no	—
754	C₂×D₄	—	47	8	no	—
755	C₂×D₄	—	47	16	no	—
756	C₂×D₄	—	47	8	no	—
757	C₂×D₄	—	47	16	no	—
758	C₂×D₄	—	47	16	no	—
759	C₂×D₄	—	47	16	no	—
760	C₂×D₄	—	94	8	no	—
761	C₂×D₄	—	94	16	no	—
762	C₂×D₄	—	94	16	no	—
763	C₂×D₄	—	94	8	no	—
764	C₂×D₄	—	94	64	no	—
765	C₂×D₄	—	94	32	no	—
766	C₂×D₄	—	94	8	no	—
767	C₂×D₄	—	94	4	no	—
768	C₂×D₄	—	94	4	no	—
769	C₂×D₄	—	94	8	no	—
770	C₂×D₄	—	188	32	no	—
771	C₂×D₄	—	188	8	no	—
772	C₂×D₄	—	188	8	no	—
773	C₂×D₄	—	188	8	no	—
774	C₂×D₄	—	188	4	no	—
775	C₂×D₄	—	188	8	no	—
776	C₂×D₄	—	188	64	no	—
777	C₂×D₄	#10625354	1	8	yes	complemented
778	C₂×D₄	C₂³×D₄₇	1	4	yes	—
779	C₂²×C₄	—	2	8	no	—
780	C₂²×C₄	—	4	8	no	—
781	C₂²×C₄	—	47	2	no	—
782	C₂²×C₄	—	47	1	no	—
783	C₂²×C₄	—	47	1	no	—
784	C₂²×C₄	—	47	1	no	—
785	C₂²×C₄	—	47	2	no	—
786	C₂²×C₄	—	47	8	no	—
787	C₂²×C₄	—	47	4	no	—
788	C₂²×C₄	—	47	4	no	—
789	C₂²×C₄	—	47	4	no	—
790	C₂²×C₄	—	47	8	no	—
791	C₂²×C₄	—	47	8	no	—
792	C₂²×C₄	—	47	8	no	—
793	C₂²×C₄	—	47	16	no	—
794	C₂²×C₄	—	47	16	no	—
795	C₂²×C₄	—	47	8	no	—
796	C₂²×C₄	—	94	4	no	—
797	C₂²×C₄	—	94	4	no	—
798	C₂²×C₄	—	94	8	no	—
799	C₂²×C₄	—	94	4	no	—
800	C₂²×C₄	—	94	8	no	—
801	C₂²×C₄	—	188	32	no	—
802	C₂²×C₄	—	188	4	no	—
803	C₂²×C₄	—	188	4	no	—
804	C₂²×C₄	—	188	8	no	—
805	C₂²×C₄	—	188	8	no	—
806	C₂²×C₄	—	188	4	no	—
807	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
808	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
809	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
810	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
811	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
812	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
813	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
814	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
815	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
816	C₄⋊C₄	—	47	8	no	—
817	C₄⋊C₄	—	47	8	no	—
818	C₄⋊C₄	—	47	8	no	—
819	C₄⋊C₄	—	47	4	no	—
820	C₄⋊C₄	—	47	4	no	—
821	C₄⋊C₄	—	47	8	no	—
822	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
823	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
824	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
825	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
826	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
827	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
828	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
829	C₂²⋊C₄	—	47	8	no	—
830	C₂²⋊C₄	—	47	8	no	—
831	C₂²⋊C₄	—	47	16	no	—
832	C₂²⋊C₄	—	47	8	no	—
833	C₂²⋊C₄	—	47	16	no	—
834	C₂²⋊C₄	—	47	8	no	—
835	C₂²⋊C₄	—	47	16	no	—
836	C₂²⋊C₄	—	47	8	no	—
837	C₂²⋊C₄	—	47	16	no	—
838	C₂²⋊C₄	—	47	8	no	—
839	C₂²⋊C₄	—	47	8	no	—
840	C₂²⋊C₄	—	47	8	no	—
841	C₂²⋊C₄	—	47	16	no	—
842	C₂²⋊C₄	—	47	16	no	—
843	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
844	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
845	C₄²	—	47	4	no	—
846	C₄²	—	47	4	no	—
847	C₄²	—	47	4	no	—
848	C₄²	—	47	16	no	—
849	C₄²	C₂³×D₄₇	1	4	yes	—
850	C₄²	C₂³×D₄₇	1	8	yes	—
851	C₂³	—	2	4	no	—
852	C₂³	—	2	4	no	—
853	C₂³	—	47	4	no	—
854	C₂³	—	47	2	no	—
855	C₂³	—	47	4	no	—
856	C₂³	—	47	8	no	—
857	C₂³	—	47	4	no	—
858	C₂³	—	94	16	no	—
859	C₂³	—	94	2	no	—
860	C₂³	—	94	2	no	—
861	C₂³	—	94	32	no	—
862	C₂³	—	94	4	no	—
863	C₂³	—	94	16	no	—
864	C₂³	—	94	8	no	—
865	C₂³	—	94	4	no	—
866	C₂³	—	94	8	no	—
867	C₂³	—	94	4	no	—
868	C₂³	—	94	4	no	—
869	C₂³	—	94	4	no	—
870	C₂³	—	94	8	no	—
871	C₂³	—	94	4	no	—
872	C₂³	—	376	32	no	—
873	C₂³	—	188	16	no	—
874	C₂³	—	188	16	no	—
875	C₂³	—	188	8	no	—
876	C₂³	—	188	32	no	—
877	C₂³	C₂×#10625354	1	8	yes	—
878	C₂³	C₂⁴×D₄₇	1	4	yes	—
879	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	4	8	no	—
882	D₄	—	94	16	no	—
883	D₄	—	94	32	no	—
884	D₄	—	94	32	no	—
885	D₄	—	94	16	no	—
886	D₄	—	94	16	no	—
887	D₄	—	94	8	no	—
888	D₄	—	94	8	no	—
889	D₄	—	94	16	no	—
890	D₄	—	188	16	no	—
891	D₄	—	188	16	no	—
892	D₄	—	188	16	no	—
893	D₄	—	188	8	no	—
894	D₄	—	188	16	no	—
895	D₄	C₂×#10625354	1	16	yes	complemented
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	8	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	4	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	16	no	—
902	C₂×C₄	—	4	16	no	—
903	C₂×C₄	—	47	2	no	—
904	C₂×C₄	—	47	4	no	—
905	C₂×C₄	—	47	2	no	—
906	C₂×C₄	—	47	2	no	—
907	C₂×C₄	—	47	4	no	—
908	C₂×C₄	—	94	8	no	—
909	C₂×C₄	—	94	4	no	—
910	C₂×C₄	—	94	2	no	—
911	C₂×C₄	—	94	2	no	—
912	C₂×C₄	—	94	4	no	—
913	C₂×C₄	—	94	2	no	—
914	C₂×C₄	—	94	8	no	—
915	C₂×C₄	—	94	16	no	—
916	C₂×C₄	—	94	8	no	—
917	C₂×C₄	—	94	16	no	—
918	C₂×C₄	—	188	8	no	—
919	C₂×C₄	—	188	8	no	—
920	C₂×C₄	—	188	16	no	—
921	C₂×C₄	—	188	16	no	—
922	C₂×C₄	—	188	8	no	—
923	C₂×C₄	C₂×#10625354	1	4	yes	—
924	C₂×C₄	#13094070	1	4	yes	—
925	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
926	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
927	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
928	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
929	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
930	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
931	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	16	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	47	4	no	—
936	C₂²	—	94	2	no	—
937	C₂²	—	94	8	no	—
938	C₂²	—	94	2	no	—
939	C₂²	—	94	4	no	—
940	C₂²	—	94	8	no	—
941	C₂²	—	94	4	no	—
942	C₂²	—	94	8	no	—
943	C₂²	—	94	4	no	—
944	C₂²	—	94	4	no	—
945	C₂²	—	94	4	no	—
946	C₂²	—	94	8	no	—
947	C₂²	—	94	4	no	—
948	C₂²	—	376	32	no	—
949	C₂²	—	188	32	no	—
950	C₂²	—	188	8	no	—
951	C₂²	—	188	16	no	—
952	C₂²	—	188	8	no	—
953	C₂²	C₂²×#10625354	1	8	yes	—
954	C₂²	C₂²×#10625354	1	2	yes	—
955	C₂²	H(5,𝔽₂)×D₄₇	1	2	yes	—
956	C₂²	C₂×#13094070	1	2	yes	—
957	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
958	C₄	—	2	4	no	—
959	C₄	—	2	8	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	4	no	—
963	C₄	—	94	2	no	—
964	C₄	—	94	4	no	—
965	C₄	—	94	2	no	—
966	C₄	—	94	2	no	—
967	C₄	—	94	4	no	—
968	C₄	C₂²×#10625354	1	4	yes	—
969	C₄	C₂×#13094070	1	4	yes	—
970	C₂	—	2	8	no	—
971	C₂	—	94	4	no	—
972	C₂	—	188	4	no	—
973	C₂	—	188	8	no	—
974	C₂	—	188	4	no	—
975	C₂	#20257421	1	4	yes	direct product factor
976	C₂	C₂³×#10625354	1	1	yes	characteristic
977	C₂	C₂×H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
978	C₂	C₂²×#13094070	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#554	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#554	D₄₇
hypocenter	C₄₇	C₂×#3519
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20257421	C₂	direct (N × H)
2. C₂×#15689839	C₂	semidirect
3. C₂×#15689826	C₂	semidirect
4. C₂×#15689821	C₂	semidirect
5. C₂×#15689795	C₂	semidirect
6. C₂×#15689764	C₂	semidirect
7. C₂×#15689764	C₂	semidirect
8. C₂×D₄×D₁₈₈	C₂	semidirect
9. C₂×D₄×D₁₈₈	C₂	semidirect
10. C₂×#15689729	C₂	semidirect
11. C₂×#15689713	C₂	semidirect
12. C₂×#15689674	C₂	semidirect
13. C₂×#15689660	C₂	semidirect
14. C₂×#15689636	C₂	semidirect
15. C₂²×#13093999	C₂	semidirect
16. C₂×#15689595	C₂	semidirect
17. C₂×C₄×D₄×D₄₇	C₂	semidirect
18. C₂×C₄₇×#554	C₂	semidirect
19. C₂²×#10625354	C₂²	semidirect
20. C₂²×#10625354	C₂²	semidirect
21. C₂³×D₁₈₈	C₂²	semidirect
22. C₂³×D₁₈₈	C₂²	semidirect
25. C₂³×C₄×D₄₇	C₂²	semidirect
26. #15689839	C₂²	semidirect
27. #15689826	C₂²	semidirect
28. #15689821	C₂²	semidirect
29. #15689795	C₂²	semidirect
30. #15689764	C₂²	semidirect
31. #15689764	C₂²	semidirect
32. D₄×D₁₈₈	C₂²	semidirect
33. D₄×D₁₈₈	C₂²	semidirect
34. #15689729	C₂²	semidirect
35. #15689713	C₂²	semidirect
36. #15689674	C₂²	semidirect
37. C₂×#13094021	C₂²	semidirect
38. C₂×#13094021	C₂²	semidirect
39. #15689660	C₂²	semidirect
40. C₂×#13094019	C₂²	semidirect
41. C₂×#13094019	C₂²	semidirect
42. C₂×#13094015	C₂²	semidirect
43. C₂×#13094013	C₂²	semidirect
44. C₂×#13094013	C₂²	semidirect
45. C₂×#13094013	C₂²	semidirect
46. #15689636	C₂²	semidirect
47. C₂×#13094009	C₂²	semidirect
48. C₂×#13094009	C₂²	semidirect
49. C₂×#13094009	C₂²	semidirect
50. C₂×#13094009	C₂²	semidirect
51. C₂×#13094000	C₂²	semidirect
53. C₂×#13093999	C₂²	semidirect
54. C₂×#13093999	C₂²	semidirect
55. C₂×#13093999	C₂²	semidirect
56. C₂×#13093999	C₂²	semidirect
57. C₂×#13093999	C₂²	semidirect
58. C₂×#13093999	C₂²	semidirect
59. C₂×#13093999	C₂²	semidirect
60. C₂×#13093999	C₂²	semidirect
61. C₂×#13093999	C₂²	semidirect
62. C₂×#13093999	C₂²	semidirect
63. C₂×#13093999	C₂²	semidirect
64. C₂×#13093998	C₂²	semidirect
65. C₂×#13093998	C₂²	semidirect
66. C₂×#13093994	C₂²	semidirect
67. C₂×#13093994	C₂²	semidirect
68. C₂×#13093994	C₂²	semidirect
69. #15689595	C₂²	semidirect
70. C₂×C₄×D₁₈₈	C₂²	semidirect
71. C₂×C₄×D₁₈₈	C₂²	semidirect
72. C₂×C₄×D₁₈₈	C₂²	semidirect
73. C₂×C₄×D₁₈₈	C₂²	semidirect
75. C₂×#13093986	C₂²	semidirect
76. C₂×#13093986	C₂²	semidirect
77. C₂×#13093986	C₂²	semidirect
78. C₂×#13093986	C₂²	semidirect
79. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
80. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
81. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
82. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
83. C₄×D₄×D₄₇	C₂²	semidirect
84. C₂×#13093982	C₂²	semidirect
85. C₂×#13093982	C₂²	semidirect
86. C₂×#13093981	C₂²	semidirect
87. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
88. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
89. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
90. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
91. C₂×C₄²×D₄₇	C₂²	semidirect
92. C₄₇×#554	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
94. C₂×#125×C₄₇	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
97. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
100. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
105. C₂×#10625354	C₂³	semidirect
106. C₂×#10625354	C₂³	semidirect
120. C₂²×D₁₈₈	C₂³	semidirect
121. C₂²×D₁₈₈	C₂³	semidirect
139. C₂²×C₄×D₄₇	C₂³	semidirect
140. #13094021	C₂³	semidirect
141. #13094021	C₂³	semidirect
142. #13094019	C₂³	semidirect
143. #13094019	C₂³	semidirect
144. #13094015	C₂³	semidirect
145. #13094013	C₂³	semidirect
146. #13094013	C₂³	semidirect
147. #13094013	C₂³	semidirect
148. #13094009	C₂³	semidirect
149. #13094009	C₂³	semidirect
150. #13094009	C₂³	semidirect
151. #13094009	C₂³	semidirect
152. #13094000	C₂³	semidirect
154. #13093999	C₂³	semidirect
155. #13093999	C₂³	semidirect
156. #13093999	C₂³	semidirect
157. #13093999	C₂³	semidirect
158. #13093999	C₂³	semidirect
159. #13093999	C₂³	semidirect
160. #13093999	C₂³	semidirect
161. #13093999	C₂³	semidirect
162. #13093999	C₂³	semidirect
163. #13093999	C₂³	semidirect
164. #13093998	C₂³	semidirect
165. #13093998	C₂³	semidirect
166. #13093994	C₂³	semidirect
167. #13093994	C₂³	semidirect
168. #13093994	C₂³	semidirect
169. C₄×D₁₈₈	C₂³	semidirect
170. C₄×D₁₈₈	C₂³	semidirect
171. C₄×D₁₈₈	C₂³	semidirect
172. C₄×D₁₈₈	C₂³	semidirect
174. #13093986	C₂³	semidirect
175. #13093986	C₂³	semidirect
176. #13093986	C₂³	semidirect
177. #13093986	C₂³	semidirect
178. C₄×C₂²⋊D₄₇	C₂³	semidirect
179. C₄×C₂²⋊D₄₇	C₂³	semidirect
180. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
181. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
182. #13093982	C₂³	semidirect
183. #13093982	C₂³	semidirect
184. #13093981	C₂³	semidirect
191. C₄⋊C₄×D₄₇	C₂³	semidirect
206. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
207. C₂²⋊C₄×D₄₇	C₂³	semidirect
208. C₂²⋊C₄×D₄₇	C₂³	semidirect
213. C₄²×D₄₇	C₂³	semidirect
219. C₄⋊Q₈×C₄₇	C₂³	semidirect
220. #125×C₄₇	C₂³	semidirect
221. C₂²⋊Q₈×C₄₇	C₂³	semidirect
222. C₂²⋊Q₈×C₄₇	C₂³	semidirect
223. C₄×Q₈×C₄₇	C₂³	semidirect
233. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
255. C₂×D₄×C₄₇	#41	semidirect
392. D₄×C₄₇	C₂×#41	semidirect
483. C₂×#554	D₄₇	semidirect
500. C₂×C₄₇	#3519	semidirect
516. #554	C₂×D₄₇	semidirect
527. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
534. C₂×#125	C₂×D₄₇	semidirect
544. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
545. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
564. C₂×C₄×Q₈	C₂×D₄₇	semidirect
585. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
590. C₄₇	C₂×#3519	semidirect
635. C₄⋊Q₈	C₂²×D₄₇	semidirect
641. #125	C₂²×D₄₇	semidirect
650. C₂²⋊Q₈	C₂²×D₄₇	semidirect
651. C₂²⋊Q₈	C₂²×D₄₇	semidirect
668. C₄×Q₈	C₂²×D₄₇	semidirect
701. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
777. C₂×D₄	#10625354	semidirect
895. D₄	C₂×#10625354	semidirect
975. C₂	#20257421	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20257421	2
C₂×#15689839	2
C₂×#15689826	2
C₂×#15689821	2
C₂×#15689795	2
C₂×#15689764	2
C₂×D₄×D₁₈₈	2
C₂×#15689729	2
C₂×#15689713	2
C₂×#15689674	2
C₂×#15689660	2
C₂×#15689636	2
C₂²×#13093999	2
C₂×#15689595	2
C₂×C₄×D₄×D₄₇	2
C₂×C₄₇×#554	2
C₂×#3519	47

Subgroups — C2×#20257421 #27124274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257421 #27124274